Fig. 4.

Training strategy for joint registration. As in Figure 2, network $h_{\theta }$ predicts an affine transform $T$ between moving and fixed images $\left\{m,f\right\}$ synthesized from label maps $\left\{s_m,s_f\right\}$. Hypernetwork ${\Gamma }_{\xi }$ takes the regularization weight $\lambda$ as input and outputs the parameters $\eta ={\Gamma }_{\xi }\left(\lambda \right)$ of network $g_{\eta }$. The moved images $m\circ T^{1/2}$ and $f\circ T^{-1/2}$ are inputs to $g_{\eta }$, which predicts a diffeomorphic warp field $\varphi$. We form the symmetric joint transform $\psi =T^{1/2}\circ \varphi \circ T^{1/2}$ by composition and compute the moved label map $s_m\circ \psi$ . Loss ${ℒ}_o$ recodes the labels of $\left\{s_m,s_f\right\}$ to optimize the overlap of select anatomy of interest—in this case brain labels only.